Libertarians have not been traditionally considered left or right. Most political surveys/quizzes that involve at least two dimensions show significant differences between libertarians and either liberals or conservatives.
In recent years there has been a trend towards somewhat of a blurring of lines between libertarians and conservatives. Part of this has been a natural response to certain policy shifts on the right, and some of it part of a deliberate campaign to coopt libertarianism by those who really aren't libertarian at all.
In the case of Syria, the push for war is coming mainly from two places: neocons who have never seen a war they didn't like, especially if they think it will help Israel (even though this probably wouldn't); and the ignorant, locker-room reactionary far right who care more about flag-waving and "looking strong" than doing what makes sense, and who will oppose anything Obama does simply because Obama did it.